Hierarchically low-rank (H-LR) matrices have been widely used to design fast solvers solvers for integral equations, boundary element methods, discretized PDEs, and kernel matrices in statistical and machine learning. These matrices include H/H2-matrices, HODLR matrices, HSS matrices and butterfly matrices. They differ in the treatment of the off-diagonal low-rank structures. These matrices can be used in iterative solvers where stuctured-matrix-vector-product is needed, or in direct solvers where structured-factorization and stuctured-solve are needed. The computational bottleneck in these types of solvers is often the construction algorithm which converts a standard dense matrix into an H-LR format. The dense matrix may not be explicitly stored. In recent advances of this field, we have seen extensive use of randomized sketching to speed up the construction process. Regardless of which H-LR formats, the common questions include: 1) which random matrix to use? 2) what size of the random matrix to use? 3) what are the error bounds of the H-LR approximation? 4) what are the key ingredients needed for high performance implementations? We will present a unified view to answer these questions, illustrate the algorithms on various applications, and discuss some open problems."